Question: $f(x) = 5x$ $g(x) = 7x^{2}-7x-3(f(x))$ $ f(g(-2)) = {?} $
Explanation: First, let's solve for the value of the inner function, $g(-2)$ . Then we'll know what to plug into the outer function. $g(-2) = 7(-2)^{2}+(-7)(-2)-3(f(-2))$ To solve for the value of $g$ , we need to solve for the value of $f(-2)$ $f(-2) = (5)(-2)$ $f(-2) = -10$ That means $g(-2) = 7(-2)^{2}+(-7)(-2)+(-3)(-10)$ $g(-2) = 72$ Now we know that $g(-2) = 72$ . Let's solve for $f(g(-2))$ , which is $f(72)$ $f(72) = (5)(72)$ $f(72) = 360$